The victim entered the Polish embassy in East Berlin with a fake bomb in order to force officials to allow him to leave the communist East for West Germany.
The Stasi agreed to let him depart and provided him with exit documents, Berlin prosecutors said in a statement.
But at the same time, it instructed the accused, a 31-year-old Stasi operative, to "neutralise" the Polish man, they said.
The victim was taken to a crossing at Friedrichsstrasse station in the heart of Berlin, accompanied by Stasi officials.
"When the 38-year-old had passed the last checkpoint in the early afternoon, the accused allegedly shot him in the back from a hiding place," prosecutors said.
The former Stasi agent has been charged with murder, and faces life in prison if convicted.
During the Cold War, the Stasi built a repressive apparatus of surveillance and intimidation, using millions of officers and informants, bugging technology and secret prisons.
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